The Department of Homeland Security is finalizing its plan for a biometric data system to track when immigrants leave the United States and will present it to Congress within "weeks," a top department official told a House Homeland Security subcommittee Tuesday.

An exit system to track who is leaving the country and when has been sought since before the Sept. 11 terrorist attacks. DHS officials, including Secretary Janet Napolitano, have agreed with the need for such a program but have previously said it would be too costly.

John Cohen, the department's deputy counter terrorism coordinator, did not discuss the cost in his testimony about the problem of immigrants who overstay visas. He said the department's report to Congress will explain how DHS plans to better determine who has overstayed their visa.

The criminal case against Amine El Khalifi, 29, of Alexandria, Va., accused in an alleged bomb plot against the U.S. Capitol, has renewed the debate about how the U.S. government -- a decade after the terror attacks of 2001 -- routinely fails to track millions of foreign visitors who remain in the country longer than they are allowed. El Khalifi was arrested in a parking lot, wearing what he thought was an explosive-laden suicide vest. He had been living illegally in the United States for 12 years.

The Obama administration doesn't consider deporting people whose only offense is overstaying a visa a priority. It has focused immigration enforcement efforts on people who have committed serious crimes or are considered a threat to public or national security.

Cohen said improvements in how data from immigrants is collected and stored has made it easier for law enforcement to identify visa overstays and determine if they pose a threat to national security or public safety.

Rep. Candice Miller, R-Mich., who led Tuesday's hearing, said El Khalifi "follows a long line of terrorists, including several of the 9/11 hijackers, who overstayed their visa and went on to conduct terror attacks." His tourist visa expired the same year he arrived from his native Morocco as a teenager in 1999.

She said 36 people who overstayed visas have been convicted of terrorism related charges since 2001.

"We have to recognize that we do have this problem," Miller said. "The truth is, in the 40 percentile of all the illegal (immigrants) are in this country on expired visas. They came in right through the front door."

El Khalifi, who is charged with attempting to use a weapon of mass destruction, never came to the attention of federal law enforcement agencies even after a series of minor run-ins with police in northern Virginia from 2002 to 2006, including disobeying a traffic sign and speeding. Programs that could have identified him if he had been jailed by local authorities, including the Security Communities program that shares fingerprints from local jails with the FBI, were not in place at the time.

The Moroccan national didn't face a felony charge -- possession of marijuana with intent to distribute -- until last September, about nine months after he became the target of the FBI probe related to the alleged plot to destroy the Capitol. He has waived his right to a preliminary hearing.

El Khalifi, unemployed when he was arrested last month, is one of an estimated millions of illegal immigrants who came to the United States with a government-issued visa and never left. He never applied to become a U.S. citizen.

Immigration and Customs Enforcement, the agency responsible for deporting illegal immigrants, has routinely combed through visa records to try to identify people who have overstayed their welcome and deport those considered threats to the community or national security.

Cohen said Tuesday that more than 37,000 people who overstayed visas were deported from 2009 to 2011

Last year, ICE reviewed a backlog of about 1.6 million suspected overstay cases involving people who had come to the U.S. since 2004. The Homeland Security Department said the review concluded that about half of those people have either left the country or applied to change their immigration status. Of the remaining half, the cases of about 2,700 people were given further review. ICE officials have not said how many of those people were deemed a national security threat or were otherwise considered priority for deportation.

For the more than 797,000 others whose cases were not reviewed further, DHS officials said their overstay status was noted in electronic files in case any of them commit crimes in the future or otherwise become a priority to be deported.

Visa overstays have long been a concern of lawmakers and law enforcement. Some estimates suggest that as many as half of the country's estimated 11 million illegal immigrants have overstayed visas.

But finding illegal immigrants who, like El Khalifi, came to the United States before biometric data was collected and records were computerized around 2004 -- and who overstayed visas but haven't committed a crime -- can be difficult, if not impossible.

"It's very difficult to find those individuals, and those individuals aren't priorities until they commit a crime," said Julie Myers Wood, who was head of ICE from 2006 to 2008.

James Ziglar, who was head of the old Immigration and Naturalization Service from 2001 until it was folded into DHS in 2002, said immigration authorities made efforts to locate immigrants thought to be a threat to national security after the Sept. 11 terrorist attacks. But simply having overstayed a visa wouldn't have made illegal immigrants like El Khalifi a priority.

"We were certainly focused on trying to find bad people and connecting the dots with the Department of State and their visa records," Ziglar said. "I doubt very seriously he (El Khalifi) would have come up on the radar. He might have if you kept drilling down further and further just because of where he was from. But he would not have been, I think, an earlier target, just because there were more suspicious types."